This article is a grammatical guide for Latex mathematical formulas in the Markdown context

This article is a grammatical guide for Latex mathematical formulas in Markdown, to help every writer to easily edit mathematical formulas in their entirety and to make them beautifully formatted.

1. Latex format in Markdown

LateX mathematical formulas come in two varieties: in-line formulas and stand-alone formulas (in-line formulas). Line formulas are mixed with other text in the text, and independent formulas are separate lines.

1.1 In-line formula

$E = MC ^ 2 $= MC2E E = MC ^ 2 E = MC2

1.2 Independent Formula

$$E = MC ^ 2 = MC2E $$E = MC ^ 2 E = MC2

2.Latex mathematical formulas

2.1 Functions, symbols, and special Characters

• index

$\exp_a b=a ^b, \exp b=e ^b, 10^m$exp⁡ab=ab,exp⁡b=eb,10m\exp_a b=a ^b, \exp b=e ^b, 10^mexpab=ab,expb=eb,10m

• logarithmic

\ln c, \lg d= \log e, \log_{10} fln ⁡c,lg⁡d=log⁡e,log⁡10f\ln c, \lg d= \log e, \log_{10} FLNC, LGD =loge,log10f

• Trigonometric functions

\sin a, \cos b, \tan c, \cot d, \ SEC e, \ CSC f sin⁡a,cos⁡b,tan⁡c,cot⁡d, SEC ⁡e, CSC f\sin a, \cos b, \tan c, \cot d, , the SEC, e, CSC fsina cosb, tanc, cotd, sece, the CSCF \ arcsin a, b \ arccos, \ arctan c arcsin ⁡ a, arccos ⁡ b, arctan ⁡ c \ arcsin a, \arccos b, \arctan carcsina,arccosb,arctanc \arccotd,\arcsece,\arccscf\ arccotd,\arcsece,\arccscf\arccot d,\arcsece,\arccscf\arccot d, \arcsece,\arccscf \arccotd,\arcsece,\arccscf \sinh a, \cosh b, \tanh c, \coth d sinh⁡a, \cosh ⁡b,tanh⁡c,coth⁡d\sinh a, \arccscf \arccotd,\arcsece,\arccscf \sinh a, \cosh b, \tanh ⁡c, \coth ⁡d\sinh a, \cosh b, \tanh c, \coth dsinha, \ coshb, \ tanhc, \ cothd \ operatorName {sh}k, \ operatorName {ch}l, \ operatorName {th}m, \ operatorname {coth} n sh ⁡ k, ch ⁡ l, th ⁡ m, coth ⁡ n \ operatorname {sh} k \ operatorname {ch} l, \ operatorname {th} m, \ operatorname {coth} NSHK, chlorophyll, THM, cothn \ operatorname {argsh} o \ operatorname {argch} p, \ operatorname {argth} q argsh ⁡ o, argch ⁡ p, argth ⁡ q \ operatorname {argsh} o \ operatorname {argch} p, \ operatorname {argth} qargsho argchp, argthq

• The absolute value

\left\vert s \right\vert∣s \left\vert s \right\vert given s

• Maximum, minimum

, min (x, y), and Max (x, y $) min ⁡ (x, y), Max ⁡ (x, y \ min (x, y), and Max (x, ymin (x, y), Max (x, y)

2.2 Limits and limits

\min x, \ Max y, \inf s, \sup tmin ⁡x, Max ⁡y,inf⁡s,sup⁡t\min x, \ Max y, \inf s, \sup minx,maxy,infs,supt \ Lim u, \ Liminf v, \limsup w lim⁡u,lim INF ⁡v, Lim sup⁡w\ Lim u, \liminf v, \lim_{x \to \infty} \frac{1}{n(n+1)} lim⁡x→∞1n(n+1)\lim_{x \to \infty} \ frac {1} {n (n + 1)} limx – up n (n + 1) 1 \ dim p \ deg q, \ det m, \ Beijing \ phi dim ⁡ p, deg ⁡ q, det ⁡ m, ker ⁡ ϕ \ dim p \ deg q, \ det m, \ Beijing \ phidimp, degq detm, ker ϕ

2.3 the projection

\Pr j, \hom l, \lVert z\ rVert, \arg zPr ⁡j,hom⁡l,∥z∥,arg⁡z\Pr j, \hom l, \lVert z\ rVert, \arg zPrj,homl,∥z∥,argz

2.4 Calculus and Derivatives

Dt, \ mathrm} {d t, \ t, partial \ nabla \ psi dt, dt, partial t, ∇ bits of dt, \ mathrm} {d t, \ t, partial \ nabla \ psidt, dt, partial t, ∇ bits

dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y dy/dx,dy/dx,dydx,dydx, partial 2 partial x1 partial x2ydy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \ frac {\ partial ^ 2} {\ partial x_1 \ partial x_2} ydy/dx, dy/dx, dx dy, dx dy, partial x1 partial x2 partial 2 y

\ prime, \ backprime, f ^ \ prime, f ‘, ‘f’, f ^ {} (3), y \ dot, \ ddot y ‘, ‵, f ‘, f ‘, ‘f’, f (3), y ˙, ¨ y \ prime, \ backprime, f ^ \ prime, F ‘, ‘f’, f ^ {} (3), y \ dot, \ ddot y ‘, ‵, f ‘, f ‘, ‘f’, f (3), y ˙, ¨ y

2.5 Class of letter symbols and constants

\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar ∞,ℵ,∁,∍,ð,Ⅎ, \infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar ∞,ℵ,∁,∍,ð,Ⅎ, \ \ eth, \ Finv, \ hbar up, ℵ, ∁, ∍, ð, Ⅎ, ℏ

, Im, and imath \ jmath, \ Bbbk, \ ell, \ mho, \ wp, \ Re, \ circledS ℑ, ı, ȷ, k, ℓ, ℧, ℘, ℜ, Ⓢ \ Im, \ imath, \ jmath, \ Bbbk, \ ell, \ mho, \ wp, \ Re, \ circledS ℑ, , , k, ℓ, ℧, ℘, ℜ, Ⓢ

2.6 operator

S_k \equiv 0 \pmod{m}sk≡0(modm) s_k \equiv 0 \pmod{m}sk≡0(modm)

A \bmod bamod ba \bmod bamodb

\ the GCD (m, n), \ operatorname {LCM} (m, n) GCD ⁡ (m, n), LCM ⁡ (m, n) \ the GCD (m, n), \ operatorname {LCM} (m, n) GCD (m, n), LCM (m, n)

, mid, and nmid \ shortmid, \ nshortmid ∣, ∤, ∣, ∤ \ mids, \ nmid, \ shortmid, \ nshortmid ∣, ∤, ∣, 

2.7 the square root of

, \ \ surd SQRT {2}, \ SQRT [n] {}, \ SQRT [3] {\ frac {x ^ 3 + y ^ 3} {2}}), 2, n, x3 + y323 \ surd, \ SQRT {2}, \ SQRT [n] {}, \ SQRT [3] {\ frac {x ^ 3 + y ^ 3} {2}}), 2, n, 32 x3 + y3

2.8 the collection

\ {\}, \ \ O the empty \ emptyset, \ varnothing {}, \ O ∅ ∅, ∅ \ {\}, \ \ empty \ emptyset, O \ varnothing {}, \ O ∅ ∅, ∅

\ in the \ notin \ not \, in \ ni, \ not \ ni ∈, ∉ ∉, ∋, ∌ \ in the \ notin \ not \ in the \ ni, \ not \ ni ∈, ∈ /  ∈, ∋,  ∋

, cap, cap, \ sqcap \ bigcap studying, ⋒, ⊓, ⋂ \ cap, \ cap, \ sqcap, \ bigcap studying, ⋒, ⊓, ⋂

, cup, cup, \ sqcup \ bigcup, \ bigsqcup, \ uplus, \ biguplus ∪, ⋓, ⊔, ⋃, ⨆, ⊎, ⨄ \ cup, \ cup, \ sqcup, \ bigcup, \ bigsqcup, \ uplus, \ biguplus ∪ ⋓, ⊔ ⋃, ⨆, ⊎, ⨄

\setminus, \ Smallsetminus, \times∖,∖,× setminus, \ Smallsetminus, \times∖,∖,×

\ subset, \ subset, \ sqsubset ⊂, ⋐, ⊏ \ subset, \ subset, \ sqsubset ⊂, ⋐, ⊏

, \ \ supset supset, \ sqsupset ⊃, ⋑, ⊐ \ supset, \ supset, \ sqsupset ⊃, ⋑, ⊐

\subseteq, \ nSubseteq, \subsetneq, \ varSubsetneq, \ sqSubseteq ⊆,⊈,⊊,⊊,⊑\ Subseteq, \ NSubseteq, \ Subsetneq, \ , \ \ varsubsetneq sqsubseteq ⊆, ⊈ ⊊, , ⊑

\supseteq, \ nSupseteq, \ Supsetneq, \varsupsetneq, \ sqSupseteq ⊇,⊉,⊋,⊋, ⊋ \ Supseteq, \ nSupseteq, \ Supsetneq, \varsupsetneq, \ sqSupseteq ⊇,⊉,⊋,⊋, ⊉ \ Supseteq, \ NSupseteq, \ Supsetneq, \ , \ \ varsupsetneq sqsupseteq ⊇ ⊉, ⊋, , ⊒

, \ \ subseteqq nsubseteqq \ subsetneqq, \ varsubsetneqq ⫅, ⊈, ⫋, ⫋ \ subseteqq, \ nsubseteqq, \ subsetneqq, \ varsubsetneqq ⫅, , ⫋, 

\ Supseteqq, \ nSupseteqq, \ Supsetneqq, \ Varsupsetneqq ⫆,⊉,⫌,⫌\ Supseteqq, \ NSupseteqq, \ Supsetneqq, \varsupsetneqq qq, \ \ nSupseteqq, \ Supsetneqq, \varsupsetneqq

2.9 the operator

The +, -, \ PM, \ mp, \ dotplus +, -, -, ∓, ∔ +, -, \ PM, \ mp, \ dotplus +, -, -, ∓, ∔

, times, and div, \ divideontimes, /, / backslash x, present, ⋇, /, \ \ times, \ div, \ divideontimes, /, / backslash x, present, ⋇, /, /

* \ \ cdot, ast, \ star, \ circ, \ bullet ⋅, ∗ ∗, ⋆, ∘, f. \ cdot, * \ ast, star, \ \ circ, \ bullet ⋅, ∗ ∗, ⋆, ∘,,

, \ \ boxplus boxminus \ boxtimes, \ boxdot ⊞, ⊟, ⊠, ⊡ \ boxplus, \ boxminus, \ boxtimes, \ boxdot ⊞, ⊟, ⊠, ⊡

, \ \ oplus ominus \ otimes, \ oslash, \ odot radius, ⊖, ⊗, ⊘, \ oplus, \ ominus, \ otimes, \ oslash, \ odot radius, ⊖, ⊗, ⊘, even

\circleddash, \circledcirc, \circledast
$\circleddash, \circledcirc, \circledast$

\bigoplus, \bigotimes, \bigodot⨁,⨂,⨀ \ Bigoplus, \bigotimes, \bigodot⨁, milk, milk

2.10 Relational symbols

= \ ne, \ neq, \ equiv, \ not \ equiv =, indicates that indicates, ≡, ≢ =, \ ne, \ neq, \ equiv, \ not \ equiv =,  =,  =, ≡,  ≡ \ doteq, \ doteqdot, ` ` \ overset {\ underset {\ mathrm {def}} {}} = {}, ` ` : = ≐, ≑ = def: = \ doteq, \ doteqdot, \ overset {\ underset {\ mathrm {def}} {}} = {}, : = ≐, ≑ = def: =

\ sim, \ nsim \ backsim, \ thicksim, \ simeq, \ backsimeq, \ eqsim, \ cong, \ ncong ~, ≁, ∽, ~, ≃, ⋍, ≂, ≅, ≆ \ sim, \ nsim, \ backsim, , \ \ thicksim, \ simeq \ backsimeq eqsim, \ cong, \ ncong ~, ≁, ∽, ~, ≃, ⋍, ≂, ≅, ≆

\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto ≈,≈,≊,≍, \approx, \thickapprox, \approxeq, \asymp, , \ \ propto varpropto material, material, ≊, ≍, ∝, ∝

< \ nless, \ ll \ not \ ll, \ name ‘LLL, \ not \ name’ LLL, \ lessdot <, ≮, fabric, the fabric ̸, ⋘, ⋘ ̸, ⋖ < \ nless, \ ll \ not \ ll, \ name ‘LLL, \ not \ name’ LLL, ≮ \ lessdot <, exploring,  exploring, ⋘,  ⋘, ⋖

> \ NGTR, \ gg, / not/gg, \ GGG, \ not \ GGG, \ gtrdot >, ≯, ≫, ≫ ̸, ⋙, ⋙ ̸, ⋗ >, \ NGTR, \ gg, / not/gg, \ GGG, \ not \ GGG, \ gtrdot >, ≯ ≫,  ≫, ⋙,  ⋙, ⋗ \ le, \ leq, \ lneq, \ leqq, \ nleq, \ nleqq, \ lneqq, \ lvertneqq, or less, or less ⪇, ≦, ≰, ≰, ≨, ≨ \ le, \ leq, \ lneq, , \ \ leqq nleq \ nleqq, \ lneqq, \ lvertneqq, or less, or less ⪇, ≦, ≰, , ≨, 

Ge, \ \ geq \ gneq, \ geqq, \ ngeq, \ ngeqq, \ gneqq, \ gvertneqq acuity, acuity, ⪈, ≧, ≱, ≱, ≩, ≩ \ ge, \ geq, \ gneq, \ geqq, \ ngeq, \ ngeqq, , \ \ gneqq gvertneqq acuity, acuity, ⪈, ≧, ≱, , ≩, 

\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless ≶,⋚,⪋,≷, ≷, , \ \ gtrless gtreqless, \ gtreqqless ≶, ⋚, ⪋, ≷, ⋛, ⪌

\leqslant, \nleqslant, \eqslantless ‘ ‘, \ Ngeqslant, \eqslantgtr ⩽, to what extent do I bless you? ≱,⪖\leqslant, \nleqslant, \eqslantless ‘ ‘, \ Ngeqslant, \ Eqslantgtr ⩽, to what extent do I bless you? \ eqslantless, \ geqslant \ ngeqslant, \ eqslantgtr ⩽, , ⪕, ⩾, , ⪖

, \ \ lesssim lnsim \ lessapprox, \ lnapprox ` ` \ gtrsim, \ gnsim, \ gtrapprox, \ gnapprox ≲, ⋦, ⪅, ⪉, ≳, ⋧, ⪆, ⪊ \ lesssim, \ lnsim, , \ \ lessapprox lnapprox \ gtrsim, \ gnsim, \ gtrapprox, \ gnapprox ≲, ⋦, ⪅, ⪉, ≳, ⋧, ⪆, ⪊

, \ \ prec nprec \ preceq, \ npreceq, \ precneqq ` ` \ succ, \ nsucc, \ succeq, \ nsucceq, \ succneqq ≺, ⊀, ⪯, ⋠, ⪵, ≻, ⊁, ⪰, ⋡, ⪶ \ prec, , \ \ nprec preceq \ npreceq, \ precneqq, \ succ, \ nsucc, \ succeq, \ nsucceq, \ succneqq ≺, ⊀, ⪯, ⋠, ⪵, ≻, ⊁, ⪰, ⋡, ⪶

\succcurlyeq, \succcurlyeq “,\ succcurlyeqsucc ≼,⋞,≽,⋟\ Preccurlyeq,\succcurlyeq, \succcurlyeq, \succcurlyeq, \ ⋟ \ curlyeqsucc ≼ ⋞, ≽

\precsim, \precnsim, \precapprox, \precnappro“\succsim, \succnsim, \succapprox, \succnapprox MEET,⋨,⪷,\ Precnappro,≿,⋩, college \ Precsim,\ precnsim, \precapprox, \succsim, \succnsim, \succapprox, \ succnapprox ≾ ⋨, ⪷, \ precnappro, ≿, ⋩, ⪸, ⪺

2.11 Geometric symbols

\parallel, \nparallel, \shortparallel, \nshortparallel,∦,∥,∦\parallel, \nparallel, \shortparallel,  \ nshortparallel ∥, ∦ ∥

\perp, \ Angle, \sphericalangle, \ Measuredangle,45 ^ circ ⊥, Angle,∢,∡,45∘\ Perp, \ Angle, \sphericalangle, \ Measuredangle, ^ \ 45 circ, coming < ∢, ∡, 45 ∘

\Box, \blacksquare, \diamond, \blacklozenge, \ Bigstar □,■,⋄,◊,⧫,★ Box, \ Blacksquare, \diamond, , Diamond, lozenge, \ blacklozenge \ bigstar -, s, ⋄, ◊ ◊, ⧫, u

\ BigcirC, triangle, BigTriangleup, \ Bigtriangledown infection,△,△,▽ bigcirc, Triangle, bigtriangleup, \ bigtriangledown ◯, delta, delta, del

\vartriangle, \triangledown“\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright △,▽,▲,▼ \blacktriangledown, \blacktriangledown, \blacktriangledown, \black triangleft, \ blacktriangleright delta del, bring about, ▼ ◀, ▶

2.12 Logical Symbols

\forall, \exists, \ Nexists ∀,∃,∄\forall, \exists, \ Nexists ∀,∃,∄\ therefore, \because, &\therefore, \ Because, \ And ∴, ∵, &

\ or \ lor \ vee, \ curlyvee \ bigvee \ or ∨ ∨, ⋎, ⋁ \ or \ lor \ vee, \ curlyvee, \ bigvee \ or ∨ ∨, ⋎, ⋁

\bar{q}, \bar{abc}, \overline{q}, \overline{abc},“\lnot \neg, \not\operatorname{R}, \bot, ABC ˉ ˉ \ top q, q ‾, ABC ‾, delivered a rope, ̸ R ⁡, coming, ⊤ \ bar {q}, \ bar {ABC}, \ overline {q}, \ overline {ABC}, \ lnot \ neg, \ not \ operatorname {R}, \ bot, , ABC \ topq ˉ ˉ, q, ABC, such types,  R, coming, ⊤

, \ \ vdash \ dashv vdash, \ vdash, \ models ⊢ ⊣, ⊨, ⊩, ⊨ \ vdash \ dashv, \ vdash, \ vdash, \ models ⊢ ⊣, ⊨, ⊩, ⊨

, \ \ Vvdash nvdash \ nvdash, \ nvdash, \ nvdash ⊪, ⊬, ⊮, ⊭, ⊯ \ Vvdash, \ nvdash, \ nvdash, \ nvdash, \ nvdash ⊪, ⊬, ⊮, ⊭, ⊯

\ulcorner \urcorner \llcorner \lrcorner ⌜⌝⌞⌟\ulcorner \urcorner \llcorner \lrcorner chrysene

2.13 the arrow

, \ \ Rrightarrow Lleftarrow ⇛, ⇚ \ Rrightarrow, \ Lleftarrow ⇛, ⇚

\Rightarrow, \nRightarrow, \Longrightarrow \implies tail,⇏,⟹⟹ \Rightarrow, \nRightarrow, \Longrightarrow \implies tail,⇏,⟹⟹

\Leftarrow, \nLeftarrow, \Longleftarrow⇐,⇍,⟸ \Leftarrow, \nLeftarrow, \Longleftarrow⇐,⇍, Longleftarrow

\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \ Iff,⇎,⟺ ⟺ \Leftrightarrow, \nLeftrightarrow, \ Longleftrightarrow \ iff as indicated by ⇎, ⟺ ⟺

\Uparrow, \Downarrow, \Updownarrow⇑,⇓,⇕ \Uparrow, \Downarrow, \Updownarrow⇑,⇓, Updownarrow⇑

\rightarrow \to, \nrightarrow, \longrightarrow→,↛,⟶\rightarrow \to, \nrightarrow, \longrightarrow→,↛,⟶

\leftarrow \gets, \nleftarrow, \longleftarrow←←,↚, 12 \ Leftarrow \gets, \nleftarrow, \ Longleftarrow ←,↚, 12

\leftrightarrow, \nleftrightarrow, \longleftrightarrow, \nleftrightarrow, \longleftrightarrow at ↮,⟷\leftrightarrow, \nleftrightarrow, \longleftrightarrow at ↮,⟷

\uparrow, \downarrow, \updownarrow↑,↓, strict quality parts \uparrow, \downarrow, \updownarrow↑,↓, \nearrow, \swarrow, \nwarrow, \ searrow ↗, ↙ ↖, ↘ \ nearrow, \ swarrow, \ nwarrow, \ searrow ↗, ↙, ↖, ↘ \ mapsto, \ longmapsto ↦, ⟼ \ mapsto, \ longmapsto ↦, ⟼

\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \ downharpoonRight \rightleftharpoons \leftrightharpoons ⇀,⇁,↼, leftrightharpoons ⇀, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, rightleftharpoons, Sunday, spade, Sunday, spade, gadget, salvation,⇋\ Rightharpoonup,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft,\upharpoonright, \downharpoonleft, \downharpoonright, , \ \ rightleftharpoons leftrightharpoons ⇀ ⇁, ↼, ↽, ↿, ↾, ⇃, ⇂, ⇌, ⇋

\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright ↶,↺, ⇈,⇉, ↺, disk \ curvearRowLeft, circlearRowLeft, \Lsh \ upuParRows, \ RightrightarRows, \ RightLeftarRows, \rightarrowtail, \ looparrowright ↶ ↺, ↰ ⇈, ⇉, ⇄, ↣, ↬ \ curvearrowright \ circlearrowright \ Rsh \ downdownarrows \ leftleftarrows \ leftrightarrows \ LeftarrowTail \ LooparrowLeft ↷,↻,↱, , \ \ leftleftarrows leftrightarrows \ leftarrowtail, \ looparrowleft ↷, ↻, ↱, ⇊, ⇇, ⇆, ↢, ↫

\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow ↪,↩,⊸,↭, ↭, ↭, ↪, hookRightarrow, HookLeftarrow, multimap, Leftrightsquigarrow, RightSquigarrow, TwoHeadRightarrow, \ twoheadleftarrow ↪ ↩, ⊸ ↭, ⇝, ↠, ↞

2.13 Special Symbols

Ellipsis: There are two common types of ellipsis in mathematical formulas, \ldots means ellipsis aligned with the bottom line of text, \cdots means ellipsis aligned with the middle line of text.

\amalg \% \dagger \ddagger \ldots \cdots ⨿%†‡… … \amalg \% \dagger \ddagger \ldots \cdots⨿%†‡… …

Smile \frown \wr \triangleleft \triangleright⌣⌢≀◃▹ \smile \frown \wr \triangleleft \triangleright⌣⌢≀◃▹

\ Diamondsuit, \ Heartsuit, \clubsuit, \ Spadesuit, \Game, \ Flat, \ Natural, \ Sharp ♢,♡, ♠,⅁,♭,♮, \ Diamondsuit, , \ \ heartsuit clubsuit \ spadesuit, \ Game, \ flat, \ natural, \ sharp ♢, ♡,, ♣ ♠, ⅁, ♭, ♮, ♯

2.14 Other symbols

\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes / ╲⋅⋉⋊⋋⋌\ Diagup \diagdown \centerdot \ ltimes \ rtimes \ leftthreetimes \ rightthreetimes ╱ ╲ ⋅ ⋉ ⋊ ⋋ ⋌

\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq
$\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq$

\intercal \barwedge \veebar \doublebarwedge \between \pitchfork ⊺⊼⊻⩞≬⋔\intercal \barwedge \veebar \doublebarwedge \ between \ pitchfork ⊺ ⊼ ⊻ ⩞ ≬ ⋔

\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright ⊲ ⊲ ⊳⋫\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright⊲ ⊳⋫ \trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq ⊴⋬⊵⋭\trianglelefteq \ ntrianglelefteq \ trianglerighteq \ ntrianglerighteq ⊴ ⋬ ⊵ ⋭

2.15 Superscript, subscript and integral, etc

^ for superscript, _ for subscript. If the contents of the ICONS are more than one character, enclose them as a whole with {}. Upper and lower indices can be nested or used simultaneously.

• superscript

a^2
$a^2$

• The subscript

a_2
$a_2$

• combination

a^{2+2}
$a^{2+2}$ a_{i,j}
$a_{i,j}$

• With the upper and lower indices

x_2^3
$x_2^3$

• Front index and subscript

{} _1 ^ 2 \! X_3 ^ 4 12 ⁣ X34 {} _1 ^ 2 \! X_3^412X34

• Derivative (HTML)

X ‘x’ x ‘x’

• Derivative (PNG)

X ^ \ ‘prime x x ^ \ primex’

• Derivative (error)

X \ prime x ‘x \ primex’

• Derivative points

{x} x ˙ \ \ dot dot {x} x ˙ \ ddot {} y y ¨ \ ddot {} y y ¨

• vector

\vec{c} (only one letter) c⃗\vec{c}c \overleftarrow{a b},\overrightarrow{c d} ab←\overleftarrow{a b}ab, CD →\ overleftrightarrow{cd} CD \overleftrightarrow{a b} ‘\widehat{e f g} ab↔ overleftrightarrow{a b}ab, efg^\widehat{e f g}efg

• The arc

(Note: \overarc is the correct word, but it doesn’t work here. Use the suggested syntax as a solution. (The {arcs} package needs to be introduced when using \ overarc.) \ overset {\ frown} {b} AB ⌢ \ overset {\ frown} {b} AB ⌢

• Top and bottom line

\overline{h I j}, \underline{k lm}hij \overline{h I j}hij, KLM ‾\underline{k lm} KLM

• In parentheses

\overbrace{1+2+\cdots+100}1+2+… +100⏞\overbrace{1+2+\cdots+100}1+2+… +100 \begin{matrix} 5050 \\ overbrace{matrix} 5050 \\ 1+2+\cdots+100} \end{matrix} 50501+2+… +100⏞\begin{matrix} 5050 \\ overbrace{1+2+\cdots+100} {matrix} \ end 50501 + 2 +… + 100

• The parentheses

\underbrace{a+b+ cdots+z} a+b+… +z⏟\underbrace{a+b+ cdots+z} a+b+… +z \begin{matrix} \underbrace{a+b+ cdots+z} \ 26 \end{matrix} a+b+… +z⏟26\begin{matrix} \underbrace{a+b+ cdots+z} \\ 26\ end{matrix} a+b+… +z26

• Sum (summation)

\ sum_ {k = 1} ^ ^ N k ∑ 2 k = 1 nk2 \ sum_ {k = 1} ^ ^ N k ∑ 2 k = 1 nk2 \ begin {matrix} \ sum_ {k = 1} ^ ^ 2 \ N k end matrix ∑ k = 1 attach nk2 \ begin {matrix} \ sum_ {k = 1} ^ ^ 2 \ N k end matrix ∑ attach nk2 k = 1

• Quadrature (multiplication)

\ prod_ {I = 1} ^ N x_i ∏ I = 1 nxi \ prod_ {I = 1} ^ N x_i ∏ I = 1 nxi \ begin {matrix} \ prod_ {I = 1} ^ N x_i \ end nxi \ {matrix} ∏ I = 1 begin {matrix} \ prod_ {I = 1} {matrix} ^ N x_i \ end ∏ nxi I = 1

• On the product

\ coprod_ {I = 1} ^ N x_i ∐ I = 1 nxi \ coprod_ {I = 1} ^ N x_i ∐ I = 1 nxi \ begin {matrix} \ coprod_ {I = 1} {matrix} ^ N x_i \ end Nxi ∐ I = 1 \ the begin {matrix} \ coprod_ {I = 1} {matrix} ^ N x_i \ end ∐ nxi I = 1

• limit

\lim_{n \to \infty}x_nlim ⁡n→∞xn\lim_{n \to \infty}x_nlimn→∞xn \begin{matrix} \lim_{n \to \infty}x_n \end{matrix} Lim ⁡n→∞xn\begin{matrix} \lim_{n \to \infty}x_n \end{matrix}limn→∞xn

• integral

\ int_ ^ {- N} {N} e ^ x \ {\} rm d x ∫ – NNex dx \ int_ ^ {- N} {N} e ^ x \ {\} rm d x ∫ – NNexdx this case \, and {} \ rm d part can be omitted, but suggest to join, can make you more beautiful. {\rm d} can be replaced with \mathrm{d} equivalently. \ begin {matrix} \ int_ ^ {- N} {N} e ^ x \ \ mathrm {matrix} {d} \ x end (the matrix integral symbol smaller) ∫ – NNex dx \ begin {matrix} \ int_ ^ {- N} {N} e ^ x \, \ mathrm {d} {matrix} ∫ x \ end – NNexdx

• Double integral

\ iint_ ^ {D} {W} \ \ mathrm {D} \, x \ mathrm {D} y ∬ DW dx dy \ iint_ ^ {D} {W} \ \ mathrm {D} \, x \ mathrm {D} y ∬ DWdxdy

• Triple integral

\ iiint_ ^ {E} {n} \ \ mathrm {d} \, x \ mathrm} {d, y \ \ mathrm {d} z ∭ EV dx dy dz \ iiint_ ^ {E} {n} \, \ mathrm {d} \, x \ mathrm {d} \, y \ mathrm {d} z ∭ EVdxdydz

• Integral of closed curve and surface

X ^ 3 \ \ oint_ {C}, \ mathrm {d} 4 x + y ^ 2 \, \ mathrm {d} y 30 Cx3 dx + 4 y2 dy \ oint_} {C ^ 3 x \, \ mathrm {d} 4 x + y \ ^ 2, \ mathrm {d} y 30 Cx3dx y2dy + 4

• intersection

\ bigcap_1 ^ 1 np \ {n} p ⋂ bigcap_1 ^ {n} p ⋂ 1 np

• And set

\ bigcup_1 ^ 1 KP \} {k p ⋃ bigcup_1 ^ {k} p ⋃ 1 KP

2.16 score

The \frac {numerator} {denominator} command is usually used to produce a fraction that can be nested. A quick ab\frac {a} {b} ba can be generated by typing \frac ab directly. If the fraction is complex, you can also use the numerator \over denominator command, where the fraction has only one layer. Effect of functional grammar | |

• score

\ frac {2} {4} = 0.5 24 = 0.5 \ frac {2} {4} = 0.542 = 0.5

• A small fraction

\tfrac{2}{4} =0.5 24=0.5\tfrac{2}{4} = 0.542=0.5

• Continuous fractions (large nested fractions)

\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
$\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a$

• Large unnested fractions

\ dfrac {2} {4} = 0.5 \ qquad \ dfrac {2} {c + \ dfrac {2} {d + \ dfrac {2} {4}}} = a 24 = 0.52 c + 2 d + 24 = a \ dfrac {2} {4} = 0.5 \ qquad C + \ \ dfrac {2} {dfrac {2} {d + \ dfrac {2} {4}}} = a42 = c + d + 4222 = 0.5 a

2.17 Binomial coefficient

• Binomial coefficient

\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr) = (nn) – r – r = Cnr = Cnn \ dbinom {n} {r} = \ binom {n} {n} – r = \ mathrm {C} _n ^ r = \ mathrm {C} _n ^} {n – r (rn) = n – (rn) = Cnr = Cnn – r

• Small binomial coefficient

\tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr) = (nn) – r – r = Cnr = Cnn \ tbinom {n} {r} = \ tbinom {n} {n} – r = \ mathrm {C} _n ^ r = \ mathrm {C} _n ^} {n – r (rn) = n – (rn) = Cnr = Cnn – r

• Large binomial coefficients

\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr) = (nn) – r – r = Cnr = Cnn \ binom {n} {r} = \ dbinom {n} {n} – r = \ mathrm {C} _n ^ r = \ mathrm {C} _n ^} {n – r (rn) = n – (rn) = Cnr = Cnn – r

Try not to use the \frac notation in exponential functions, limits, and integrals with base E: it makes the whole function look strange and can be ambiguous. This is why it almost never appears in professional mathematical typesetting. Write these fractions horizontally, using slash intervals/(slash lines instead of score lines).

Example:

\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \\
\hline \\
e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\
\int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\
\end{array}
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Display ::: : hlJs-center

$\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}$

: : :

2.18 Matrices, conditional expressions, equations

Grammar:

\begin{type} Formula contents \end{type}Copy the code

The types can be matrix matrix pmatrix bmatrix bmatrix vmatrix vmatrix, conditional expression cases, multi-line alignment equations aligned, and array array.

In formula content: Insert & in each line to specify what you want to align, and use \ line wrap at the end of each line.

• Wu kuang matrix

Use begin{matrix} at the beginning, end{matrix} at the end, insert matrix elements in the middle, insert & between each element, and use \\ at the end of each line.

\begin{matrix}
x & y \\
z & v
\end{matrix}
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hljs-center

$\begin{matrix} x & y \\ z & v \end{matrix}$

• A box matrix

Replace matrix with pmatrix bmatrix bmatrix vmatrix vmatrix at the beginning.

\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}
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$\begin{vmatrix} x & y \\ z & v \end{vmatrix}$

\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}
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$\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}$

Use \cdots,… \cdots,… \ddots,… \cdots,… \vdots,…. \cdots.

\begin{bmatrix}
0      & \cdots & 0      \\
\vdots & \ddots & \vdots \\
0      & \cdots & 0
\end{bmatrix}
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$\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}$

\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
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$\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$

\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
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$\begin{pmatrix} x & y \\ z & v \end{pmatrix}$

2.19 Conditional expressions

f(n) =
\begin{cases} 
n/2,  & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}
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$f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}$

2.20 Multi-line equations and congruences

People often want a neat, central sequence of equations. Use \ begin} {aligned… } {\ end aligned.

\begin{aligned}
f(x) & = (m+n)^2 \\
     & = m^2+2mn+n^2 \\
\end{aligned}
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$\begin{aligned} f(x) & = (m+n)^2 \\ & = m^2+2mn+n^2 \\ \end{aligned}$

\begin{alignedat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
     & = m^2-2mn+n^2 \\
\end{alignedat}
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$\begin{alignedat}{3} f(x) & = (m-n)^2 \\ f(x) & = (-m+n)^2 \\ & = m^2-2mn+n^2 \\ \end{alignedat}$

2.21 equations

\begin{cases}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
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$\begin{cases} 3x + 5y + z \\ 7x – 2y + 4z \\ -6x + 3y + 2z \end{cases}$

or

\left\{\begin{aligned}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{aligned}\right.
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$\left\{\begin{aligned} 3x + 5y + z \\ 7x – 2y + 4z \\ -6x + 3y + 2z \end{aligned}\right.$

2.22 Arrays and tables

In general, a formatted table is more readable than plain text or typeset text. Both arrays and tables begin with \begin{array}, followed by the number of columns and text alignment attributes for each column, c L R for center, left, and right, respectively. If a vertical line, to be inserted in the insert | defined type, if you want to insert the horizontal line, insert \ hline before the next line input. Like a matrix, you insert & between each row of elements, ending each row with \\ and ending the array with \end{array}. Example 1:

\ begin {array} {c | the LCR} n & \ text {left-aligned} & \ text {center alignment} & \ text {right-aligned} \ \ \ hline 1 & 0.24 125 \ \ & 1 & 2 & & - 1 & 189-8 \ \ & 3 -20 & 2000 & 1+10i \end{array}Copy the code

Display: N the left center alignment right-aligned 10.2411252-1189-83-2020001 + 10 I \ begin {array} {c | the LCR} n & \ text {left-aligned} & \ text {center alignment} & \ text {right-aligned} \ \ \ 1 & hline 0.24&1&125 \\ 2&-1 &189&-8 \\ 3&-20&2000&1 + 10I \end{array}n123 left aligned 0.24−1−20 center aligned 11892000 right aligned 125−81+ 10I

Example 2:

\begin{array}{lcl}
z        & = & a \\
f(x,y,z) & = & x + y + z 
\end{array}
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Display: z = af (x, y, z) = x + y + z \ begin & = {array} {LCL} z & a \ \ f (x, y, z) & = & x + y + z \ end {array} zf (x, y, z) = = ax + y + z

Example 3:

\begin{array}{lcr}
z        & = & a \\
f(x,y,z) & = & x + y + z    
\end{array}
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Display: z = af (x, y, z) = x + y + z \ begin & = {array} {the LCR} z & a \ \ f (x, y, z) & = & x + y + z \ end {array} zf (x, y, z) = = ax + y + z

Example 4:

\begin{array}{ccc}
a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
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Display: abS001011101110\begin{array}{CCC} A & b & S \\ \hline 0&0&1\\ 0&1\\ 1&1&0\\ end{array}a0011b0101S1110

2.23 Nested arrays or tables

Multiple arrays/tables can be nested within each other to form a set of arrays/tables. You must declare the $$symbol before using nesting. Example:

% outer vertical array of Arrays \begin{array}{C} % Inner horizontal array of Arrays \begin{array}{cc} % The lining of the inner array of minimum values \ "minimum" array begin {array} {c | CCCC} \ text {min} & 0 and 1 & 2 & 3 \ \ \ hline & & & & 0 0 0 0 0 \ \ 1 &0&1&1&1 \\ 2&0&1&2&2 \\ 3&0&1&2&3 \end{array} &% inner array of maximum values \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 {array} \ \ end end {array} % inner end group of the first line form \ \ % inner array of delta values inside the second line of the delta value array \ begin {array} {c | CCCC} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} % Inner row 2 table group End \end{array}Copy the code

Display: % outer vertical array of Arrays \begin{array}{C} % Inner horizontal array of Arrays \begin{array}{cc} % The lining of the inner array of minimum values \ “minimum” array begin {array} {c | CCCC} \ text {min} & 0 and 1 & 2 & 3 \ \ \ hline & & & & 0 0 0 0 0 \ \ 1 &0&1&1&1 \\ 2&0&1&2&2 \\ 3&0&1&2&3 \end{array} &% inner array of maximum values \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 {array} \ \ end end {array} % inner end group of the first line form \ \ % inner array of delta values inside the second line of the delta value array \ begin {array} {c | CCCC} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} % Inner row 2 table group End \end{array}

2.24 Use arrays to implement matrices with partition symbols

Example:

\left[
    \begin{array}{cc|c}
      1&2&3\\
      4&5&6
    \end{array}
\right]
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Display:

Cc | c representatives in a three columns of the matrix between the second and third column in the insert line.

2.25 the brackets

(), [] and | symbol itself, use the \ {\} {}.

• Short brackets

\frac{1}{2}
$\frac{1}{2}$

• Long braces

\left(\frac{1}{2} \right)
$\left(\frac{1}{2} \right)$

Use \left and \right to create (parentheses), [square brackets] and {curly braces} that automatically match the height

• Parentheses, little parentheses

\left( \frac{a}{b} \right)
$\left( \frac{a}{b} \right)$

• Square brackets, middle brackets

\left[ \frac{a}{b} \right]
$\left[ \frac{a}{b} \right]$

• Curly braces, curly braces

\left{ \frac{a}{b} \right}

\left{ \frac{a}{b} \right}

• Angle brackets

\left \langle \frac{a}{b} \ Right \rangle⟨ AB ⟩\left \ Langle \ FRAc {a}{b} \right \rangle⟨ BA ⟩

• Single vertical line, absolute value

\ left | \ frac {a} {b} \ right | ∣ ab ∣ \ left | \ frac {a} {b} \ right | ∣ ∣ ∣ ba ∣ ∣ ∣

• Double vertical line, Van

\ left \ | \ frac {a} {b} \ right \ | ∥ ab ∥ \ left \ | \ frac {a} {b} \ right \ | ∥ ∥ ∥ ba ∥ ∥ ∥

• Integral function

\left \ lFloor \frac{a}{b} \right \rfloor⌊ ab⌋\left \lfloor \frac{a}{b} \right \rfloor⌊ba⌋

• Top function

\left \lceil \frac{c}{d} \right \rceil⌈ CD ⌉\left \ LCeil \frac{c}{d} \right \rceil⌈dc⌉

• Slash and backslash

\left / \frac{a}{b} \right \backslash
$\left / \frac{a}{b} \right \backslash$

• Up and down arrow

\left / \frac{a}{b} \right \backslash
$\left / \frac{a}{b} \right \backslash$

• Mixed brackets

\left[0,1 \right)[0,1) \left[0,1 \right)[0,1)

• Single left parenthesis

\left \{\frac{a}{b} \right.
$\left \{\frac{a}{b} \right.$

• Single right parenthesis

\left. \frac{a}{b} \right \}
$\left. \frac{a}{b} \right \}$

You can use \big, \big, \bigg, \bigg to control the size of parentheses, Such as code \ tightly (\ tightly [\ Big \ {\ Big \ langle \ left | \ | \ frac {a} {b} \ | | \ \ right Big \ rangle \ Big \} \ tightly] \ tightly showed: ([{⟨ ∣ ∥ ab ∥ ∣ ⟩}]) \ tightly (\ tightly [\ Big \ {\ Big \ langle \ left | \ | \ frac {a} {b} \ | | \ \ right Big \ rangle \ Big \} \ tightly] \ tightly ) ([{⟨ ∣ ∣ ∣ ∥ ba ∥ ∣ ∣ ∣ ⟩}])

2.28 color

Use \color{color}{text} to change a specific text color. Changing the text color requires browser support, and if the browser doesn’t know what color you want, the text will be rendered black.

\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & & &
\verb+#00F+ & \color{#00F}{text} & & \\
& & \verb+#0F0+ & \color{#0F0}{text} &
& & \verb+#0FF+ & \color{#0FF}{text}\\
\verb+#F00+ & \color{#F00}{text} & & &
\verb+#F0F+ & \color{#F0F}{text} & & \\
& & \verb+#FF0+ & \color{#FF0}{text} &
& & \verb+#FFF+ & \color{#FFF}{text}\\
\hline
\end{array}
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$\begin{array}{|rrrrrrrr|}\hline \verb+#000+ & \color{#000}{text} & & & \verb+#00F+ & \color{#00F}{text} & & \\ & & \verb+#0F0+ & \color{#0F0}{text} & & & \verb+#0FF+ & \color{#0FF}{text}\\ \verb+#F00+ & \color{#F00}{text} & & & \verb+#F0F+ & \color{#F0F}{text} & & \\ & & \verb+#FF0+ & \color{#FF0}{text} & & & \verb+#FFF+ & \color{#FFF}{text}\\ \hline \end{array}$